Exploiting Chaos in Oversampled A/D Converters.
Final technical rept. 1 Jul 93-31 Dec 95,
CALIFORNIA UNIV BERKELEY
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The aim of this research project was to alleviate the tone problem in sigma delta modulators by exploiting chaos and unstable limit cycles. This was achieved by designing encoders with open loop poles outside the unit circle. A side effect of this approach is the possibility of the modulator becoming unstable, i.e., of the internal states becoming unbounded. An analysis of the stability characteristics and the tonal properties of the chaotic double loop sigma delta modulator was presented. Bounds on maximum internal states were determined. It was shown that the tone behavior of the double loop sigma delta modulator is improved when the poles are moved outside the unit circle however, not all spectral peaks are removed. A mechanism for tone generation was identified and general spectral characteristics as a function of pole location were obtained. It was shown that there is a trade off between stability, tonal behavior and signal to noise ratio performance. Audio testing along with a series of simulations were also performed to compare the efficacy of pole placement with that of the more traditional tone removal technique of dithering. Based on the results, design guidelines were presented. In addition to the above results, a switched capacitor implementation of the double loop sigma delta modulator with open loop poles outside the unit circle was considered. Initial testing of the integrated circuit verified some of the theoretical results on the tonal behavior of the double loop sigma delta modulator.